Huddersfield possess the Premier League's fourth worst defence this season, leaving them third from bottom of the table.
Heaton, meanwhile, has fallen down the pecking order at Burnley, after Joe Hart's arrival from Manchester City in the summer transfer window.
And the Sun claims the three-cap England international is desperate to leave Turf Moor, where another Three Lions shot-stopper, Nick Pope, is also employed.
Heaton's Burnley contract only has 18 months left to run, and the presence of both Hart and Pope could tempt the Clarets into selling the 32-year-old.
A move to Huddersfield, who are based just 25 miles east of Burnley, could appeal to Heaton, whose roots are in the north west.
Jonas Lossl and Ben Hamer have shared the Terriers' goalkeeping duties this season.
Would Heaton be a good addition for Huddersfield?